The crowdsourcing used in this thread to identify 4 SuperJ aircraft (see wiki) with wifi appears to have been successful, BA have confirmed that only 4 aircraft have operating wifi at the moment. However they have told Trade and Speedbird:
Originally Posted by BA
For a limited period thanks to our partner Visa, we are offering all customers flying on a Wi-Fi enabled aircraft one hour of free browsing connectivity until the end of January. If the aircraft is enabled, an announcement will be made by the cabin crew and instructions will be available on how to register and log on by joining the ‘BA Wi-Fi’ network.